How to prove that $$x^{2^n}+x+1$$ is irreducible in $F_2$
-Is this question relevant to finite field?
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@CalvinLin It might still be the product of two smaller degree polynomials (which also have no roots in $\mathbb F_2$). – Hagen von Eitzen Dec 31 '12 at 11:35
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1You might be interested in this http://math.stackexchange.com/questions/122274/why-xpn-x1-is-irreducible-in-mathbbf-p-only-when-n-1-or-n-p-2 – Ram Dec 31 '12 at 11:37
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@HagenvonEitzen Yes, I realized that soon after, when I tried factoring it. – Calvin Lin Dec 31 '12 at 11:39
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You can't prove it because it's not true: $x^8+x+1 = (x^2+x+1)(x^6+x^5+x^3+x^2+1)$.
TonyK
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thanks. This problem is from my textbook on Abstract Algebra. I find that book has many errors. – Li Xinghe Dec 31 '12 at 11:59